Answer: 42 degrees (choice B)
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How I got this answer:
The alternate exterior angles (7x-2) and (6x+18) are congruent due to the fact that line s is parallel to line t.
Set the two expressions equal to one another. Solve for x
7x-2 = 6x+18
7x-2+2 = 6x+18+2 .... adding 2 to both sides
7x = 6x+20
7x-6x = 6x+20-6x .... subtracting 6x from both sides
x = 20
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If x = 20, then we can find the measure of angle (7x-2)
7x-2 = 7*20-2 = 140-2 = 138
As a check, let's see what angle (6x+18) is too
6x+18 = 6*20+18 = 120+18 = 138
We get the same result for each angle, so that confirms x = 20 is correct.
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Since angle (7x-2) is 138 degrees, this means
angle 1 = 180 - (7x-2)
angle 1 = 180 - 138
angle 1 = 42 degrees
